# Question

Formatted question description: https://leetcode.ca/all/272.html

 272	Closest Binary Search Tree Value II

Given a non-empty binary search tree and a target value,
find k values in the BST that are closest to the target.

Example:

Input: root = [4,2,5,1,3], target = 3.714286, and k = 2

4
/ \
2   5
/ \
1   3

Output: [4,3]

Note:

Given target value is a floating point.
You may assume k is always valid, that is: k ≤ total nodes.
You are guaranteed to have only one unique set of k values in the BST that are closest to the target.

Assume that the BST is balanced, could you solve it in less than O(n) runtime (where n = total nodes)?

Hint:

1. Consider implement these two helper functions:
i. getPredecessor(N), which returns the next smaller node to N.
ii. getSuccessor(N), which returns the next larger node to N.
2. Try to assume that each node has a parent pointer, it makes the problem much easier.
3. Without parent pointer we just need to keep track of the path from the root to the current node using a stack.
4. You would need two stacks to track the path in finding predecessor and successor node separately.

@tag-tree


# Algorithm

This tree is considered balanced if: the difference between heights of the left subtree and right subtree is not more than 1.

### In-order

The comparison is completed during the in-order traversal.

When traversing to a node,

• If the result array is less than k at this time, add this node value directly to the result,
• If the absolute value of the difference between the node value and the target value is less than the absolute value of the difference between the first element of the result and the target value, indicating that the current value is closer to the target value, delete the first element and add the current node value to the end,
• On the contrary, it means that the current value deviates more from the target value than all the values in the result res. Due to the characteristics of the in-order traversal, the subsequent values will deviate further, so the final result is directly returned at this time

### Heap

A pair of difference diff and node value stored in the heap.

In order to traverse the binary tree (other traversal methods can also be used), and then calculate the absolute value of the difference between the target value and the target value for each node value. Due to the nature of the maximum heap, the largest diff is automatically the first to maintain k pairs, if If there are more than k, delete the big pair at the front of the heap, and remove the node value in the pair for the k pairs left and store it in the result.

Java